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A287146
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Number of partitions of n into distinct parts such that the absolute difference between any part and the sum of all smaller parts is not larger than one.
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2
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1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2
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OFFSET
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0,14
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LINKS
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FORMULA
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a(2^n) = 0 for n > 0.
a(2^n-1) = 1 for n >= 0.
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EXAMPLE
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a(3) = 1: 21.
a(13) = 2: 6421, 7321.
a(25) = 3: (12)6421, (12)7321, (13)6321.
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MAPLE
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b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
b(n, i-1)+`if`(i>n or abs(i-(n-i))>1, 0, b(n-i, i-1))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..120);
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[i(i+1)/2 < n, 0, If[n == 0, 1, b[n, i - 1] + If[i > n || Abs[i - (n - i)] > 1, 0, b[n - i, i - 1]]]];
a[n_] := b[n, n];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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